Magnetic resonance (quantum mechanics)
Due to the static field, the dipole can assume a number of discrete energy eigenstates, depending on the value of its angular momentum (azimuthal) quantum number.
The oscillating field can then make the dipole transit between its energy states with a certain probability and at a certain rate.
When the frequency of that field leads to the maximum possible transition probability between two states, a magnetic resonance has been achieved.
; the result obeys Schrödinger equation: States with definite energy evolve in time with phase
A special case occurs where a system oscillates between two unstable levels that have the same life time
[1] If atoms are excited at a constant, say n/time, to the first state, some decay and the rest have a probability
; The rate of decay of atoms from state two is proportional to the number of atoms present in that state, while the constant of proportionality is decay constant
Performing the integration rate of decay of atoms from state two is obtained as: From this expression many interesting points can be exploited, such The existence of spin angular momentum of electrons was discovered experimentally by the Stern–Gerlach experiment.
In that study a beam of neutral atoms with one electron in the valence shell, carrying no orbital momentum (from the viewpoint of quantum mechanics) was passed through an inhomogeneous magnetic field.
This process was not approximate due to the small deflection angle, resulting in considerable uncertainty in the measured value of the split beam.
As shown in the figure, the source emits a beam of neutral atoms, having spin angular momentum
) will deviate downward (path 1), i.e. to the region of less magnetic field B, to minimize energy.
In the region between the poles of magnet 3, atoms having 'upward' spin get upward push and atoms having 'downward' spin feel downward push, so their path remains 1 and 2 respectively.
is applied in the region between poles of magnet 2, produced by oscillating current in circular coils then there is a probability for the atoms passing through there from one spin state to another (
[clarification needed] The atoms that transition from 'upward' to 'downward' spin will experience a downward force while passing through magnet 3, and will follow path 1'.
, where g is 'Landé g factor'), 'Landé g-factor' is obtained which will enable one to have correct value of magnetic moment
This experiment, performed by Isidor Isaac Rabi is more sensitive and accurate compared than Stern-Gerlach.
Spin angular momentum allows magnetic resonance phenomena to be explained via classical physics.
Classical electrodynamics tells us that torque on a magnetic dipole of moment
, a high precession amplitude allows the magnetic moment to be completely flipped.
The origin of this correspondence is that the evolution of the expected value of magnetic moment is identical to that obtained by classical reasoning.
In magnetic resonance imaging (MRI) the spin angular momentum of the proton is used.
The most available source for protons in the human body is represented by hydrogen atoms in water.
applied to water causes the appearance of two different energy levels for spin angular momentum,
than the other way, causing absorption of microwave or radio-wave radiation (from the rotating field).
When the field is withdrawn, protons tend to re-equilibrate along the Boltzmann distribution, so some of them transition from higher energy levels to lower ones, emitting microwave or radio-wave radiation at specific frequencies.
Instead of nuclear spin, spin angular momentum of unpaired electrons is used in EPR (electron paramagnetic resonance) in order to detect free radicals, etc.
The phenomenon of magnetic resonance is rooted in the existence of spin angular momentum of a quantum system and its specific orientation with respect to an applied magnetic field.
Both cases have no explanation in the classical approach and can be understood only by using quantum mechanics.
Since the basic elements of magnetic resonance have no classical origin, although analogy can be made with classical Larmor precession, MR should be treated as a quantum phenomenon.
